Question

A chemist wants to mix some 45% alloy with some 55% alloy to produce 30 ounces of a 51% alloy. How many ounces of each strength should he use?

Answer 1

Thank you so much in advance! :)

Answer 2

45% is the same as multiplying by 0.45, 55% is the same as multiplying by 0.55 and 51% is the same as multiplying by 0.51

you have 51% of 30 ounces

0.51 x 30

(which equals) made up of 45% of one alloy, plus 55% of the other.

0.45 x alloy1
+
0.55 x alloy2

so

0.51 x 30 = 0.45 x alloy1 + 0.55 x alloy2

you want the total to be 30 ounces, so the amount you use of alloy1, plus the amount of alloy 2 should equal 30

so you have the two equations.

30 = alloy1 + alloy 2
0.51 x 30 = 0.45 x alloy1 + 0.55 x alloy2

which you can solve as simultaneous equations either gaussian or substitution.

Answer 3

thx :)